As a first contribution, I developed a new notion of quantum nondeterministic computation based on quantum finite automata. Using this notion I introduced the first cryptographic protocol based on quantum automata and studied its properties in great depth. This research, thus, lays the theoretical foundations for future quantum and nano technologies that could offer securities in its execution and implementation.In order to develop improved cryptographic and communication protocols based on quantum automata, I realized that a more thorough understanding of the computational model was required. Towards that end, I introduced a novel notion of conciseness for quantum automata called "state complexity". With this new complexity measure, I studied in great depth the fundamental properties of space-bounded quantum computers and developed new techniques for its analysis. These results could potentially be extrapolated to quantum communication and cryptography.The obtained results unearthed several properties of communication and cryptographic protocols whose underlying model of computation are quantum automata. Given the current scaling problems of computational resources that the development of quantum computers faces, a solid theoretical foundation of quantum automata helps in the understanding of what we can and cannot do given the limited resources we have.